Semi-analytic Continuum Spectra of Type II Supernovae

We extend the approximate radiative transfer analysis of Hershkowitz, Linder, and Wagoner (1986) to a more general class of supernova model atmospheres, using a simple fit to the effective continuum opacity produced by lines (Wagoner, Perez, and Vasu 1991). At the low densities considered, the populations of the excited states of hydrogen are governed mainly by photoionization and recombination, and scattering dominates absorptive opacity. We match the asymptotic expressions for the spectral energy density Jat the photosphere, whose location at each frequency is determined by a first-order calculation of the deviation of Jfrom the Planck function B�. The emergent spectral luminosity then assumes the form L� = 4π 2 r 2 ζ 2 B�(Tp), where Tp(ν) is the photospheric temperature, ζ is the dilution factor, and r∗ is a fiducial radius (ultimately taken to be the photospheric radius rp(ν)). The atmosphere is characterized by an effective temperature Te (∝ L 1/4 r −1/2 ∗ ) and hydrogen density nH = n∗(r∗/r) � ; and less strongly by the heavy element abundance and velocity gradient. Our major result is the dependence of ζ on frequency ν and the parameters Tp, rp, and α. The resulting understanding of the dependence of the spectral luminosity on observable parameters which characterize the relevant physical conditions will be of particular use in assessing the reliability of the expanding photosphere method of distance determination. This is particularly important at cosmological distances, where no information about the progenitor star will be available. This technique can also be applied to other low-density photospheres.